The present disclosure is directed to a method and apparatus for characterizing and correcting misdirected imaging flux in an imaging system.
All imaging systems experience stray light flux. Imaging systems are victimized by phenomena that misdirect a small portion of the entering flux to undesired locations in the image. The term “imaging systems” as used herein includes, for example, optical systems, x-ray systems, and computerized tomography systems. Among optical systems of particular interest are digital-camera optics, telescopes, and microscopes. Other systems that do not employ the directional passage of flux, such as magnetic resonance imaging systems, also fall within the term “imaging systems.” Depending on the type of imaging system, the “image” may have a single dimension (a linear image), two dimensions (a planar image), three dimensions (a volume image), or more dimensions (a hyper image). In the most general sense the misdirected flux may be termed “stray-flux,” although in the context of different systems, it is known by different terms such as “stray-light.” Though it will be employed frequently throughout the present specification, particularly in conjunction with the illustrative embodiment, it should be appreciated that the term “stray-light” is synonymous with “stray-flux” for applications in which the latter terminology is more appropriate, or by other terms appropriate to their field of application.
Optical imaging systems may include many factors that misdirect a small portion of the entering light flux to undesired locations in the image plane. Among possible causes, these factors include but are not limited to: 1) Fresnel reflections from optical-element surfaces, as noted in U.S. Pat. No. 6,829,393, which typically result in ghost images, 2) diffraction at aperture edges, 3) scattering from air bubbles in transparent glass or plastic lens elements, 4) scattering from surface imperfections on lens elements, 5) scattering from dust or other particles, and 6) flux originating in focal planes other than the plane of interest. The misdirected flux, which is called by the terms “stray light,” “lens flare”, “veiling glare”, “haze,” and by other names, degrades both the contrast and the photometric accuracy of the image. For example, in photography, back-lighted scenes such as portraits that contain a darker foreground object suffer from poor contrast and reduced detail of the foreground object. In three-dimensional fluorescence microscopy that employs deconvolution for object reconstruction, stray fluorescence flux originating from planes other than that of interest can degrade the contrast of image detail and, in some cases, effectively obscure that detail.
Stray light also affects the color accuracy of an image. P. A. Jansson and R. P. Breault referred to a traditional simple manipulation of offset and gain, or contrast that can lessen subjective objections to stray-flux contaminated images. These manipulations, however, do not correct the underlying flaw in the image and do, in fact, introduce additional error. For a complete discussion of the effect of stray light on color accuracy, see Jansson, P. A., and Breault, R. P. (1998). “Correcting Color-Measurement Error Caused by Stray Light in Image Scanners,” The Sixth Color Imaging Conference: Color Science, Systems, and Applications, Nov. 17-20, 1998, Scottsdale, Ariz., pp. 69-73.
U.S. Pat. No. 5,153,926, assigned to the assignee of the present disclosure, describes various embodiments of a method to remove the stray-flux effect from images. This method demands significant amounts of computation. Prior referenced U.S. Pat. No. 6,829,393 also assigned to the assignee of the present disclosure, describes a particularly efficient method and apparatus for effecting such removal. The method may be implemented within the imaging apparatus itself, a digital camera for example. Accurate removal of stray-flux effects first requires determination of the image forming system's property of misdirecting image-forming flux. More explicitly, the stray light point-spread function (PSF) of the system is required.
The PSF of an imaging system may be described by an integral. For a planar object, the flux imparted may be described by the function o(x, y), which may be emitted from a spatially varying source of flux whose magnitude o varies with Cartesian coordinates x and y. Also, the source may be a reflective, transmissive, fluorescent or other object from which flux emanates with similarly varying magnitude. Generally, all of the flux emanating from the object falls within bounds on x and y, and the area of the object plane confined by those bounds may be called the object field. An imaging device, such as a camera lens, including all of its optical, mechanical and electrical components, may convey flux from the object plane onto an image plane. The magnitude of the flux falling on the image plane may be defined by the function i(x, y). Generally all of the flux falling upon the image plane originates from the object. The flux quantities conveyed by various portions of the imaging device add in the detector plane by linear superposition such that a function s(x, x′; y, y′) characterizes the imaging device and the functioning of the imaging process is generally described by the integral Equation (1).i(x,y)=∫∫s(x,x′;y,y′)o(x,y)dx′dy′  (1)The function s(x, x′; y, y′) is designated as the PSF of the imaging system. In general, the mathematical expression for s comprises all contributions that may be identified. For example, contributions include (1) the behavior of a hypothetically perfect imaging system that would realize the image i as a perfect replication of the object o, though possibly spatially scaled, (2) diffractive spreading owing to the finite aperture of the imaging device, (3) aberrations arising from non-ideal aspects of device design, device fabrication materials limitations, or imperfect device fabrication or alignment, thereby giving rise to redistribution of flux, (4) so-called stray light or stray flux arising from flux misdirection such as Fresnel reflections and scattering as noted in the foregoing. Depending on the physical nature of these contributions and their interactions, combining them may employ simple addition, convolution, or other mathematical means.
Although a two-dimensional integral is used to describe the behavior of an imaging system, a one-dimensional integral may be similarly employed without any loss of generality by mere redefinition of the imaging kernel function s. This approach is discussed in “Deconvolution of Images and Spectra,” p. 85. Academic Press, New York, 1997. Similarly, Equation (1) is applicable to stray flux and analogous effects in other systems, including those not employing the directional passage of flux, regardless of dimensionality, by redefining s. Only the central core of a camera's full point-spread function corresponds to the more traditional point-spread function.
Generally, such a PSF, i.e., s or its components, may be determined via experiment, directly or indirectly, or by a theoretical analysis or modeling calculation based on the design of the imaging system. That is, the PSF may take the form of, or be derived from, certain response coefficients, which may be calculated based on the imaging system's design as noted in U.S. Pat. No. 5,153,926. In the case of an optical imaging system, formulas based on the laws of physics and/or experimental data may be used for theoretical analysis to determine the PSF. Alternately, computer software designed to perform optical ray tracing may be employed for the required calculations. TracePro by Lambda Research Corporation of Littleton, Mass. and LightTools by Optical Research Associates of Pasadena, Calif. are two examples of such computer software. Such calculations, however, because they are based on the design of the system and not on its physical embodiment, may not account for all relevant physical effects. This approach requires a high level of specialized skill to perform the needed calculations.
Also, in any given system, the PSF may be determined directly. Experimentally in principle, introducing a highly localized source of optical flux as an object, a so-called point-source object, produces the PSF directly in output image plane. Because only a small fraction of the incident flux is typically misdirected to any particular undesired location in the image plane, an intense flux source must be employed. The intense source, in turn, typically causes image-plane detector saturation, thereby directly preventing PSF measurement in the region of saturation. This saturation may also interfere with proper signal processing, and thus prevent or greatly complicate determination of the PSF from the measured signal values.
Signal processing may be employed to indirectly determine the PSF of a given system. The imaging performance of both spectrometers and optical imaging systems has long been characterized by employing the concept of a PSF. Traditionally, this PSF has incorporated mainly contributions from aperture diffraction, optical aberrations, and possibly defocus blur. This traditional PSF is relatively compact and localized compared with the PSF associated with stray flux and, unlike the stray-flux PSF, has long been a mainstay of optical system design and analysis. In both spectroscopy and optical imaging, traditional PSF's have been successfully determined by introducing a known object, sometimes a flux source that is not highly localized. PSF determination by these means requires removal of broadening and other effects introduced by the objects extended (not point-like) nature. More specifically, because these objects are extended, the acquired image data contain contributions from both the PSF and the object. The acquired data need to be processed to remove the object contribution, thereby leaving only the PSF.
For an optical system exhibiting a shift-invariant imaging characteristic, objects exhibiting a straight discrete boundary or edge may be used to determine the transfer function of the optical system as described in Tatian, B. (1965). “Method for Obtaining the Transfer Function From the Edge Response Function,” J. Opt. Soc. Am. 55, 1014-1019. The PSF is easily obtained from this function by computing its Fourier transform. A discussion of the relationships between edge- and line-spread and point-spread functions, and mathematical expressions relevant to PSF determination via these means is provided in “Radiologic Imaging,” 2-Vol. Ed., V. 1, Barrett, H. H. and Swindell, W., pp. 59-61. Academic Press, New York, 1981. In thus determining a PSF, it is helpful if the PSF is shift-invariant and rotationally symmetric.
If the PSF is not symmetric or has a lower order of symmetry, or if the PSF is shift variant, methods employing edge and line response become more complicated and may not be able to accurately characterize the PSF. Furthermore, because a shift-variant PSF exhibits more degrees of freedom than a shift-invariant one, more data is required for an accurate determination. Stable inversion of a shift-variant imaging equation to obtain the shift-variant PSF may not be possible based merely on the characteristics of the known object plus limited data available.